No the “state issued non-drivers license ID card” is specifying a particular document, not a class of IDs. That is, for those individuals who aren’t licensed to drive states issue an official ID. That’s what they’re allowing for there.

In Michigan our concealed carry permits are actually issued by County, but as has been pointed out the requirements for obtaining one are more stringent than those for a DL so it’d stand to reason a person who knows how to recognize the markings built into them for security/authenticity’s sake would accept, but most people aren’t trained in those markings.

I don’t think it’s an anti-2A reason they’re not taking it. Heck most ANTIs don’t even know it requires a background check to buy a gun much less that a license is required to carry one concealed.